OFFSET
0,3
COMMENTS
Partial sums of powers of 64 (A089357), a.k.a. q-numbers for q=64.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..500
Quynh Nguyen, Jean Pedersen, and Hien T. Vu, New Integer Sequences Arising From 3-Period Folding Numbers, Vol. 19 (2016), Article 16.3.1. See Table 1.
Index entries for linear recurrences with constant coefficients, signature (65,-64).
FORMULA
From Wolfdieter Lang, Apr 08 2022: (Start)
a(n) = Sum_{j=0..n-1} 2^(6*j). See the comment.
G.f.: x/((1 - 64*x)*(1 - x)).
E.g.f.: exp(x)*(exp(63*x) - 1)/63. (End)
MATHEMATICA
LinearRecurrence[{65, -64}, {0, 1}, 20] (* Harvey P. Dale, Aug 20 2017 *)
PROG
(Magma) [(64^n-1)/63: n in [0..20]]; // Vincenzo Librandi, Aug 10 2011
(PARI) A133853(n)=64^n\63
(Maxima) makelist((64^n-1)/63, n, 0, 20); /* Martin Ettl, Nov 12 2012 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Jan 07 2008
EXTENSIONS
a(6)-a(15) from Vincenzo Librandi, Aug 10 2011
STATUS
approved